Recent advances in computer-assisted analysis of polymer processing show the need for an accurate description of the material's behaviour under the effect of stress and temperature. In this work, for thermoforming applications, we were interested in characterizing the subsidence of circular thermoplastic high-density polyethylene (HDPE) membranes under the combined effect of temperature and gravity. For this purpose, a modified Burgers model with three viscous parameters was considered to represent the appropriate behaviour of the thermoplastic membrane. The identification of the mechanical parameters of the material was carried out using an approach combining experimental results, numerical simulation and optimization. Finally, the thermodependency of membrane viscosity was studied using two thermal models, Arrhenius’ law and the William-Landel-Ferry equation (WLF).